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Are boys better at math?

There definitely tend to be more male scientists, and in general males are more numerous than females in math-heavy fields. Is this because boys are better at math, which is the foundation for all these fields?

This post examines whether this is the case. And if boys are better at math, then is it due to biological or environmental factors? Can we do something to change this, or is it just how we evolved?

The metric most often used to measure a difference in performance by boys and girls is called Cohen’s d. It basically measures how many standard deviations boys are better than girls in the given sample. Obviously, negative values then indicate that girls are better than boys. An absolute d of 0.20 is considered small, 0.20 to 0.50 is a medium difference, and above 0.50 we have a strong difference.

Lots of studies have compared boy vs. girl math performance. We have huge samples (in the millions), and meta-studies (an examination of many previous studies to draw an overall conclusion) too. The general picture that emerges is that we have a very low d. We basically have no difference in lower grades. In higher grades, the effects are somewhat ambiguous, but in any case differences are small.

These studies, however, are not international (most of them are U.S.-based). If we look at cross-country differences in d, we can totally rule out a biological effect. If we assume that people don’t dffer much biologically across countries (a reasonable assumption), then all cross-country variance in d can be attributed to the environment. Indeed, there are countries with high d‘s, and even countries with negative d‘s. So there clearly is a variation in the math gap that is due to the environment.

But what countries have low d‘s? The ones with high gender equality? No, not really. Gender equality and related measures (such as number of females in the legislature, etc.) are not really good predictors of d. Matter of fact, Muslim Middle Eastern countries, where women tend to have limited rights, have very low d‘s. Political correctness thus doesn’t seem to help. (Indeed, it has been shown in other studies that females in countries with very high gender equality (like Scandinavian countries) have more of a tendency to go into stereotypically female occupations.)

So in sum, we do have gender differences in math scores, and environment is a determinant of them. But gender equality is not what we should think of when we say environment. Note though, that this is not to say that biological explantions can be ruled out.

But if d‘s are low, thus differences are nonexistant in most U.S. studies, then why do we have considerably more males in STEM fields in the U.S.? Consider another interesting phenomenon: boys tend to be influenced more by peer effects. If you put a boy and a girl who perform equally well in a median school to a bad school, then the boy will be more likely to give in to peer pressure (which in this case would mean developing anti-school attitudes). Thus boys in bad schools tend to perform worse than girls. But this works the other way around as well. If you put the same boy and girl in an elite school, the boy will be more likely to outperform the girl (because peer pressure is now driving students to study more).

In other words, boys tend to become unpopular if they focus on academics in a bad school, whereas girls not so much. This seems to work the other way around as well. We could expect then that boys have a greater variance in their test scores. If boys and girls are equal in a median school, boys are worse at a bad school, but they are better at an elite school, then boys will have a larger variance in their test scores.

The variance ratio (VR) of boys’ math scores to girls’ math scores indicate that this is indeed the case. VR tends to be somewhere between 1.1 and 1.2. A VR of 1 would indicate no difference in variance, a VR above 1 indicates more variance for boys. This could explain why we see more boys in STEM fields: because at the top of the class boys do outperform girls in math. But is this really the case?

Bessudnov and Makarov (2013) study over 700,000 Russian students who took a standardized college entrance exam in math, the United State Examinations (USE). Their sample has a d of 0.05, or practically no test score difference between boys and girls on average, and a VR of 1.12, which are both in the range suggested by previous studies. The authors look at the top of the distribution, i.e. at the top students to see if there is any differences there. First note the distributon of scores by gender below.

You can clearly see that indeed boys are more likely to be in either of the tails (or extreme ends) of the distribution. In Russia, like in probably any country, urban schools tend to be better, more elite than rural schools. Students from higher socio-economic status tend to attend them, and they generally foster a better academic atmosphere than rural schools. The authors find that the test score gap is higher in oblasts (which are kind of like US states) with a higher proportion of students enrolled in urban schools.

In other words, oblasts with more good schools tend to have higher differences. So indeed this seems to confirm that boys tend to outperform girls at the top of the distribution. But Bessudnov and Makarov (2013) get better evidence than this. They look at the data on the school level by quantile.

This means that they look at all the students who are in the 95th percentile (i.e. among the top 5%) at their school, then basically inspect the math score difference in this subsample. They find strong evidence that boys do outperform girls, but they can only do so at the very top of the distribution.

On average (i.e. for all students) there is absolutely no difference between boys and girls, if anything girls tend to somewhat outperform boys. If the authors look at the whole sample of schools, and only certain percentiles (i.e. bottom 5%, top 5%), then they still cannot find a score gap. But when they look at only the best quality schools (identified by their type, or by the fact that they’re in the cities), then we can see a big difference. Boys outperform girls at these schools, especially among the top students.

Since it is probably the best students in math who end up specializing in STEM fields, this can potentially explain the abundance of boys in these fields. Now, why this is happening is an interesting question. I would say that this effect cannot possibly be driven by gender inequality or anything related to it. What seems to matter is that boys react differently, more sensitively, to peer pressure.

This of course is not to say that there is no discrimination acting against girls. But the difference in reacting to peer pressure between boys and girls (and thus the larger variance of boys) has been shown in other contexts as well. So the results do appear to be mainly driven by a well-established phenomenon.

Unless one accepts some degree of innate difference (whether favoring boys or girls), the only way discrimination could fully explain this pattern of math gaps is if there was discrimination against boys at the low end of the distribution, no discrimination in the middle, and discrimination against girls at the high end. This seems unintuitive and implausible.

On a side note: this sort of also confirms that the infamous comments made by Larry Summers were – given the current state of research – true. At least, he was talking exactly about what peer-reviewed, published papers have shown. Summers’ critics (on this issue) thus appear to be not scientifically, but politically motivated.